Automatic differentiation in geophysical inverse problems

Automatic differentiation (AD) is the technique whereby output variables of a computer code evaluating any complicated function (e.g. the solution to a differential equation) can be differentiated with respect to the input variables. Often AD tools take the form of source to source translators and produce computer code without the need for deriving and hand coding of explicit mathematical formulae by the user. The power of AD lies in the fact that it combines the generality of finite difference techniques and the accuracy and efficiency of analytical derivatives, while at the same time eliminating 'human' coding errors. It also provides the possibility of accurate, efficient derivative calculation from complex 'forward' codes where no analytical derivatives are possible and finite difference techniques are too cumbersome. AD is already having a major impact in areas such as optimization, meteorology and oceanography. Similarly it has considerable potential for use in non-linear inverse problems in geophysics where linearization is desirable, or for sensitivity analysis of large numerical simulation codes, for example, wave propagation and geodynamic modelling. At present, however, AD tools appear to be little used in the geosciences. Here we report on experiments using a state of the art AD tool to perform source to source code translation in a range of geoscience problems. These include calculating derivatives for Gibbs free energy minimization, seismic receiver function inversion, and seismic ray tracing. Issues of accuracy and efficiency are discussed

A combined geochemical and μCT study on the CO2 reactivity of Surat Basin reservoir and cap-rock cores: porosity changes, mineral dissolution and fines migration

Geological storage of CO generally involves injection of a CO stream into a high porosity and permeability reservoir, contained by one or more overlying low permeability formations. Sandstone reservoirs and associated cap-rocks of targeted CO storage sites therefore have distinct properties such as porosity and mineral contents. Their geochemical response or reactivity to injected supercritical CO and associated changes in porosity, and permeability affecting scaling, mineral trapping, injectivity, or migration can therefore be very different. Six drill core samples including quartz-rich sandstones, calcite cemented sandstones, and feldspar or clay-rich cap-rocks from a proposed demonstration site in the Surat Basin, Australia, were characterized before and after reaction with pure supercritical CO and low salinity formation water. The quartz-rich sandstones have low reactivity, and maintain high porosities with visible pore connectivity after reaction, they are unlikely to be affected by scaling. Kaolin and fine grain movement observed via μCT and SEM could have the potential to open or plug pores, potentially increasing or decreasing permeability and CO injectivity. Calcite cemented sandstones had the greatest measured change in porosity after reaction via calcite dissolution. Narrow angular channels were formed in the calcite cement around framework grains, extending through to the center of the sub-plug in the courser grained rock, and surface roughness increased. Solution pH was however quickly passivated. The highest concentrations of Ca, Mn, Sr, and Mg were released to solution from calcite dissolution. Clay (and feldspar) rich cap-rock core had mainly microporosity and the smallest initial pore throat diameters associated with clays. Small changes to μCT calculated porosities after reaction were related to a decrease in chlorite X-ray density, and dissolution of patchy carbonate minerals. Pores were disconnected in μCT images, except for some created horizontal connection along a sandy lamination in a cap-rock. Dissolved concentrations of Ca, Fe, Si, Sr, Mn, Li and Mg increased via dissolution of both carbonate and silicate minerals. Dissolved Ca, Fe, Mn and Mg from silicate minerals in the cap-rock were available for longer term mineral trapping of CO. Potential increases in porosity and migration will be highest in the calcite cemented zones, while clay-rich cap-rocks could be expected to maintain integrity. There is a low likelihood of mineral trapping or scaling in the quartz rich lower Precipice Sandstone. Overlying rocks can provide Fe, Mg, Ca for mineral trapping of CO as ferroan carbonates such as siderite, ankerite and dolomite over longer time scales when pH is buffered. Changes to porosity, mineral content, and water chemistry after pure CO reaction observed here and in other published studies were dependent on mineral content and fluid accessibility. These results could be generalized to other sandstone reservoirs where it is expected to inject CO. The results can also be used to validate geochemical models to build longer term predictions

A fresh approach to investigating CO2 storage: Experimental CO2-water-rock interactions in a low-salinity reservoir system

The interactions between CO2, water and rock in low-salinity host formations remain largely unexplored for conditions relevant to CO2 injection and storage. Core samples and sub-plugs from five Jurassic-aged Surat Basin sandstones and siltstones of varying mineralogy have been experimentally reacted in low-salinity water with supercritical CO2 at simulated in situ reservoir conditions (P=12MPa and T=60°C) for 16days (384h), with a view to characterising potential CO2-water-rock interactions in fresh or low-salinity potential siliclastic CO2 storage targets located in Queensland, Australia. CO2-water-rock reactions were coupled with detailed mineral and porosity characterisation, obtained prior to and following reaction, to identify changes in the mineralogy and porosity of selected reservoir and seal rocks during simulated CO2 injection. Aqueous element concentrations were measured from fluid extracts obtained periodically throughout the experiments to infer fluid-rock reactions over time. Fluid analyses show an evolution of dissolved concentration over time, with most major (e.g. Ca, Fe, Si, Mg, Mn) and minor (e.g. S, Sr, Ba, Zn) components increasing in concentration during reaction with CO2. Similar trends between elements reflect shared sources and/or similar release mechanisms, such as dissolution and desorption with decreasing pH. Small decreases in concentration of selected elements were observed towards the end of some experiments; however, no precipitation of minerals was directly observed in petrography. Sample characterisation on a fine scale allowed direct scrutiny of mineralogical and porosity changes by comparing pre- and post-reaction observations. Scanning electron microscopy and registered 3D images from micro-computed tomography (micro-CT) indicate dissolution of minerals, including carbonates, chlorite, biotite members, and, to a lesser extent, feldspars. Quantitative mineral mapping of sub-plugs identified dissolution of calcite from carbonate cemented core, with a decrease in calcite content from 17vol.% to 15vol.% following reaction, and a subsequent increase in porosity of 1.1vol.%. Kinetic geochemical modelling of the CO2-water-rock experiments successfully reproduced the general trends observed in aqueous geochemistry for the investigated major elements. After coupling experimental geochemistry with detailed sample characterisation and numerical modelling, expected initial reactions in the near-well region include partial dissolution and desorption of calcite, mixed carbonates, chloritic clays and annite due to pH decrease, followed in the longer-term by dissolution of additional silicates, such as feldspars. Dissolution of carbonates is predicted to improve injectivity in the near-well environment and contribute to the eventual re-precipitation of carbonates in the far field

Great Artesian Basin authigenic carbonates as natural analogues for mineralisation trapping

This project is the first to comprehensively investigate the controls on the formation of authigenic carbonates in low salinity, siliciclastic aquifers of the Great Artesian Basin. These processes are\ua0natural analogues for mineralisation trapping of CO2 during geo-sequestration. Calcite is the main carbonate present. Analyses included elemental composition, C and O stable isotopes, fluid inclusion analyses including\ua0gas isotopes, SEM-EDS and QEMSCAN, and X-ray micro-CT scanning.\ua0The samples reflect\ua0a variety of fluid origins, compositions, and temperatures of precipitation.\ua0Differentiating between carbonate formed via different mechanisms, and determining controls on the extent of authigenic carbonate formation, could lead to options for engineered accelerated mineralisation in reservoirs

Some remarks on generalised multipole expansions

Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed by Šebek some years ago [J. Šebek, Czech. J. Phys. B 38, 1185 (1988)];
the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry